利用等价无穷小替换求极限时应注意的问题  

Problems of Limit Value Through Equivalent Infinitesimal Substitution

作　　者：黄星 张倩瑶 Huang Xing;Zhang Qianyao(Nanyang Vocational College, Nanyang 474500, China)

机构地区：[1]南阳职业学院,河南南阳474500

出　　处：《黑龙江科学》2021年第13期130-131,共2页Heilongjiang Science

摘　　要：通过若干例子讨论了利用等价无穷小替换求极限时应注意的几个问题:被替换的量在取极限时其极限必须为零;对于分子分母中的乘积因子,可以放心使用等价无穷小替换。若分子或分母是两个等价无穷小之和或差,应慎用此种方法。计算00型未定式的极限时,使用等价无穷小替换要比其他方法简单。The problems of limit value through equivalent infinitesimal substitution through several examples need attention,i.e.we should make sure the limit value of substitution quantity be zero,and use equivalent infinitesimal substitution at ease when getting product factor in the numerator and denominator.If the numerator and denominator are the sum or difference of two equivalent infinitesimals,we should think carefully before using the method.When calculating the limit value of 00 indeterminate form,it is easier to use equivalent infinitesimal substitution than other methods.

关 键 词：等价无穷小替换 极限 

分 类 号：O171[理学—数学]